Areas that teemed with thousands of excited spectators during the London 2012 Olympics will reopen to the public as landscaped parklands housing outdoor art installations from 5 April.

James Corner, the architect responsible for the much-praised High Line urban park in New York, has overseen the landscaping of the south end of the Queen Elizabeth Olympic Park, where the stadium and aquatics centre are sited.

The London Legacy Development Corporation (LLDC) – the City Hall body responsible for making the most of the £8.7bn public investment in the Games – said the reopening of the end of the park closest to the Westfield shopping centre and Stratford transport links was a "huge moment in our vision to create a new heart of east London".

The chief executive, Dennis Hone, said: "With beautiful parklands and waterways, and world-class sporting facilities the Park will become a must-visit destination for everyone – local people and visitors alike. We would encourage everyone to come and explore more from 5 April."

The £22.3m ArcelorMittal Orbit, the 115-metre-high Anish Kapoor sculpture that towers over the 560 acres of the Olympic Park, and still divides opinion, will reopen to visitors on the same date.

Hone, who has previously said the south end of the Park would be London's answer to Copenhagen's Tivoli Gardens, has spoken of his desire to attract three overlapping constituencies - local people, visitors from across London and tourists from outside the capital.

The LLDC said more than 1 million people had already visited the park since sections reopened last year. Most attended summer concerts on the site, where the first housing developments are now being built, or went to the Anniversary Games in the Olympic stadium.

A large children's play area has also opened near the velodrome, while BT Sport has moved into the former media centre.

The Lee Valley VeloPark will open in March, allowing public access to the velodrome where Sir Chris Hoy won his gold medals; there will also be a new cycle track and a BMX track.

The velodrome will host elite competition, with riders including the 2012 medallist Laura Trott competing in the Revolution track cycling series on 14 and 15 March.

The Zaha Hadid-designed aquatics centre, now stripped of the wings that increased its capacity during the Olympics, will reopen to the public on 1 March, and will host a mixture of public sessions and elite events in its two 50-metre pools.

But the £429m Olympic stadium, undergoing a controversial £154m refit to make it suitable for football and athletics, will reopen fully only in the summer of 2016. However, it will host five rugby World Cup games in summer 2015 during a pause in construction.

The London mayor, Boris Johnson, who must convince that the park and its proposed 6,800 houses will deliver for residents in the borough of Newham and the city as a whole, insisted the plans already outstripped those of any other Olympic host city.

"Queen Elizabeth Olympic Park has delivered an astonishing legacy, and reopening the south part of the park will delight thousands of Londoners and visitors to our city," he said.

"No other Olympic city has come close to London's success in delivering a lasting legacy of sporting venues, jobs, homes and simply wonderful parklands."

Chobham Academy, the school on the fringes of the park, welcomed its first pupils in September last year, and in November the first residents started moving into the 2,818 flats that once made up the athletes' village.